If you have resources at your disposal, use them. Ask the desk clerk at the hotel you are staying in or check the Internet for local things you can do in spite of the rain. You may be surprised to find that there is a wide variety of great things you can experience, even if you have to cancel your original plans.
You always have the option of just grabbing an umbrella and keeping with your original plans. Take walk on the beach when it's raining. Check out the local fare as long as the rain isn't too torrential. If you don't mind dealing with the unexpected weather and you're willing to get a little wet, then go ahead and keep your plans. Everything will still be the same, only wet.
This may be a great opportunity to check out some of the tourist spots that you thought would be too busy to visit. If you're like a lot of travelers you might have planned on avoiding some so-called "tourist traps" because of the massive numbers of people you would likely encounter. With a rainy day you might be able to see these places after all because the majority of people who had planned on going will probably cancel their plans. Head off to the amusement park, go see the monument and just work around the rain.
There are plenty of places you can go that won't be affected by rain at all. Indoor events such as museums and indoor sporting events are great things to do when it's raining outside. Be flexible and switch some of your plans around. You can do all the outdoor things another day when it isn't raining.
Declare a day of rest and relaxation. Too often people get so wrapped up in keeping a hectic vacation schedule that they don't set aside any time to just enjoy being on vacation. If you're staying at a nice hotel there will probably be a spa you can visit, so consider getting pampered. Of course, you can just stay in bed all day and order room service if you would like. Remember, it's your vacation. If rain forces you to stay in for the day, embrace your opportunity to get some well deserved rest.
